Research

Generally, I work in scientific computing and mathematical modeling.

My Diplom and Ph.D. research focuses on physics-based modeling and includes solids mechanics and fracture simulation as well as inverse parameter and interface estimation. During the cause of my research I have gained solid knowledge about PDEs and inverse problems. I further have extensive experience with the finite element method (FEM), the level set method, and embedded interfaces. My research also includes investigations into collisions, the material point method (MPM), and mesh-cutting algorithms.

My postdoctoral research was on efficient simulations of electric power grids and agent-based decentralized optimization of operational management for distribution grids.

Most of my research code is written in C++, including a variety of packages and libraries, e.g. OpenMP, Boost, VTK, and many more. I have also used Java, Matlab and some Python for prototyping.

I have successfully worked independently by myself as well as in teams. In these teams, I have been both member and team leader.


Distribution Grid Optimization / Smart Grids

At the University of Kassel I was involved in various projects that focus on distribution grid optimization and the development of future smart grids. Some of these are listed below:

OpSim: development of a versatile co-simulation and test framework that allows connecting different power grid components, including a real-time grid simulator, via standardized interfaces

DREAM: a novel heterarchical management approach of complex electrical power grids, providing new mechanisms for stable and cost effective integration of distributed renewable energy sources

Netz:Kraft: this project will investigate new ways for grid restoration after a black out event for power grids with a high penetration of renewable distributed energy resources (DER) by including them in active support roles

PrIME: innovative probabilistic methods for energy system technology


Fracture Simulation

3D Dynamic Level Set Fracture:


Abstract:

We utilize the shape derivative of the classical Griffith’s energy in a level set method for the simulation of dynamic ductile fracture. The level set is defined in the undeformed configuration of the object, and its evolution is designed to represent a transition from undamaged to failed material. No re-meshing is needed since the resulting topological changes are handled naturally by the level set method. We provide a new mechanism for the generation of fragments of material during the progression of the level set in the Griffith’s energy minimization. Collisions between different material pieces are resolved with impulses derived from the material point method over a background Eulerian grid. This provides a stable means for colliding with embedded interfaces. Simulation of corotational elasticity is based on an implicit finite element discretization.

J. Hegemann, C. Jiang, C. Schroeder, J. Teran, A Level Set Method for Ductile Fracture, ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA), pp. 193-201, 2013. [view][pdf] [website]

This paper was awarded the Best Passive Animation Paper Award (sponsored by Intel) at ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) 2013!

XFEM (2D):

Abstract:

We present a method for simulating quasistatic crack propagation in 2-D which combines the extended finite element method (XFEM) with a general algorithm for cutting triangulated domains, and introduce a simple yet general and flexible quadrature rule based on the same geometric algorithm. The combination of these methods gives several advantages. First, the cutting algorithm provides a flexible and systematic way of determining material connectivity, which is required by the XFEM enrichment functions. Also, our integration scheme is straightfoward to implement and accurate, without requiring a triangulation that incorporates the new crack edges or the addition of new degrees of freedom to the system.

C. Richardson, J. Hegemann, E. Sifakis, J. Hellrung, and J. Teran. An XFEM method for modeling geometrically elaborate crack propagation in brittle materials, International Journal for Numerical Methods in Engineering, 2011; 1097-0207. [view][pdf][website]


Inverse Constitutive Modeling


Abstract:

We introduce a general and efficient method to recover piecewise constant coefficients occurring in elliptic partial differential equations as well as the interface where these coefficients have jump discontinuities. For this purpose, we use an output least squares approach with level set and augmented Lagrangian methods. Our formulation incorporates the inherent nature of the piecewise constant coefficients, which eliminates the need for a complicated non-linear solve at every iteration. Instead, we obtain an explicit update formula and therefore vastly speed up computation. We employ our approach to the example problems of Poisson's equation and linear elasticity and provide the combination of simultaneously recovering coefficients and interface.

J. Hegemann, A. Cantarero, C. Richardson, and J. Teran. An explicit update scheme for inverse parameter and interface estimation of piecewise constant coefficients in linear elliptic PDEs, SIAM Journal on Scientific Computing, 35(2), pp. A1098-A1119, 2013. [view][pdf][website]